Bangdiwala's B

Bangdiwala's B statistic was created by Shrikant Bangdiwala in 1985 and is a measure of inter-rater agreement.Bangwidala S (1985) A graphical test for observer agreement. Proc 45th Int Stats Institute Meeting, Amsterdam, 1, 307–308Bangdiwala K (1987) Using SAS software graphical procedures for the observer agreement chart. Proc SAS User's Group International Conference, 12, 1083-1088 While not as commonly used as the kappa statistic the B test has been used by various workers.Grill E, Mansmann U, Cieza A, Stucki G (2007) Assessing observer agreement when describing and classifying functioning with the International Classification of Functioning, Disability and Health. J Rehabil Med 39(1):71-76Ossa XM, Munoz S, Amigo H, Bangdiwala SI (2010) Secular trend in age at menarche in indigenous and nonindigenous women in Chile. Am J Hum Biol 22(5):688-694Jenkins V, Solis-Trapala I, Langridge C, Catt S, Talbot DC, Fallowfield LJ (2011) What oncologists believe they said and what patients believe they heard: an analysis of phase I trial discussions. J Clin Oncol 29(1):61-68 Bangdiwala SI, Haedo, AS, Natal, ML, Villaveces A (2008) The Agreement Chart as an Alternative to the Receiver-Operating Characteristic Curve for Diagnostic Tests. J Clin Epidemiol 61, 866–874 While it is principally used as a graphical aid to inter observer agreement, its asymptotic distribution is known.

Definition

The test is applicable to testing the agreement between two observers. It is defined to be

$B = \frac$

where $n_$ are the values on the main diagonal,
$n_$ is the $i$th row total, and
$n_$ is the $i$th column total of the contingency table.
The value of B varies in value between 0 (no agreement) and +1 (perfect agreement).

In large samples B has a normal distribution whose variance has a complicated expression.Bangdiwala, Shrikant I. (1988
"The Agreement Chart"
Department of Biostatistics,University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 1859 (Appendix) For small samples a permutation test is indicated.

Guidance on its use and its extension to ''n'' x ''n'' tables have been provided by Munoz & Bangdiwala.Munoz SR & Bangdiwala SI (1997) Interpretation of Kappa and B statistics measures of agreement. J Applied Stats 24 (1) 105-112 It may be more useful than the more commonly used Cohen's kappa in some circumstances.Shankara V & Bangdiwala SI (2008) "Behavior of agreement measures in the presence of zero cells and biased marginal distributions". ''Journal of Applied Statistics'', 35 (4), 445-464

Tutorials and examples

Worked examples of the use of Bangdiwala's B have been published.
The statistical programming language R has a set of functions that will compute the B test, and a tutorial on the use of a test using these R functions is available.Friendly, M.
"Working with categorical data with R and the vcd and vcdExtra packages"
CRAN R project website.

See also

* Cohen's kappa
* Fleiss' kappa
* Scott's Pi

References

{{statistics

Comparison of assessments
Categorical variable interactions